In this paper, we propose and analyze a spectral approximation for the numerical solutions of fractional integro-differential equations with weakly kernels. First, original are transformed into an equivalent singular Volterra integral equation, which possesses nonsmooth solutions. To eliminate singularity solution, introduce some suitable smoothing transformations, then use Jacobi collocation m...

Volterra subdiffusion problems with weakly singular kernel describe the dynamics of processes well. The graded L1 scheme is often chosen to discretize such since it can handle singularity solution near $$t = 0$$ . In this paper, we propose a modification. We first split time interval [0, T] into $$[0, T_0]$$ and $$[T_0, T]$$ , where $$T_0$$ ( $$0< T_0 < T$$ ) reasonably small. Then, applied in ...

In this paper, existence, uniqueness and continuity of the adapted solutions for neutral stochastic delay Volterra equations with singular kernels are discussed. In addition, continuous dependence on the initial date is also investigated. Finally, stochastic Volterra equation with the kernel of fractional Brownian motion is studied to illustrate the effectiveness of our results.

The effect of non-stationary external forces on the vibration pipelines made composite materials is investigated in paper. A mathematical model pipeline developed, considering viscosity properties structure and base material, axial forces, internal pressure, resistance disturbances. viscoelastic conveying fluid under vibrations constructed based Boltzmann-Volterra integral model. to study a Eul...